%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE035+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:43:03 AM UTC 2026
% Result : Theorem 73.99s 17.16s
% Output : Refutation 60.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 118 ( 62 unt; 0 typ; 4 def)
% Number of atoms : 253 ( 140 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1011 ( 105 ~; 61 |; 35 &; 787 @)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 129 !; 3 ?; 136 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(complement_decl,type,
complement: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( B @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( D @ c @ ( B @ ( A @ addition ) @ ( C @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( zero @ ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( C @ c @ ( sk1 @ ( B @ multiplication ) @ multiplication ) @ leq ) )
& ( B @ test )
& ( C @ test ) )
=> ( zero @ ( C @ c @ ( A @ ( sk1 @ addition ) @ ( B @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( zero @ ( B @ c @ ( sk2 @ ( A @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( B @ c @ ( sk1 @ ( A @ multiplication ) @ multiplication ) @ leq ) )
& ( A @ test )
& ( B @ test ) )
=> ( zero @ ( B @ c @ ( sk2 @ ( sk1 @ addition ) @ ( A @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( zero @ ( A @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( A @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( sk3 @ test )
& ( A @ test ) )
=> ( zero @ ( A @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[51]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(83,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(84,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[84]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
<=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(77,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(86,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( B @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( D @ c @ ( B @ ( A @ addition ) @ ( C @ multiplication ) @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( B @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( D @ c @ ( B @ ( A @ addition ) @ ( C @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( B @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( D @ c @ ( B @ ( A @ addition ) @ ( C @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
( ~ ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( sk3 @ test )
& ( sk4 @ test ) ),
inference(cnf,[status(esa)],[19]) ).
thf(23,plain,
zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ),
inference(cnfConj,[status(thm)],[20]) ).
thf(22,plain,
~ ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(115,plain,
( ( ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,22]) ).
thf(116,plain,
( ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(125,plain,
( ( zero != zero )
| ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(132,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(531,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[132,31]) ).
thf(532,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[531]) ).
thf(584,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ),
inference(simp,[status(thm)],[532]) ).
thf(611,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= sk1 ) ),
inference(simp,[status(thm)],[584]) ).
thf(640,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= sk1 ),
inference(simp,[status(thm)],[611]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[42]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[27]) ).
thf(122,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,23]) ).
thf(128,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c ) )
| ( ( sk1 @ ( sk3 @ multiplication ) )
!= zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(129,plain,
( ( ( sk1 @ ( sk3 @ multiplication ) )
!= zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(278,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,129]) ).
thf(279,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(285,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk3 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(287,plain,
( ( sk3 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(105,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( sk4 @ c @ ( zero @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,22]) ).
thf(109,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( sk3 != zero )
| ~ ( zero @ ( sk4 @ c @ ( zero @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(113,plain,
( ( sk3 != zero )
| ~ ( zero @ ( sk4 @ c @ ( zero @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(228,plain,
( ( sk3 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(rewrite,[status(thm)],[113,28]) ).
thf(669,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk3 != zero )
| ~ $true
| ( sk3 != zero ) ),
inference(paramod_ordered,[status(thm)],[287,228]) ).
thf(670,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[669]) ).
thf(671,plain,
sk3 != zero,
inference(pattern_uni,[status(thm)],[670:[]]) ).
thf(78,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[77]) ).
thf(79,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[78]) ).
thf(288,plain,
~ ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) ),
inference(rewrite,[status(thm)],[22,31]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(35,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(25,plain,
sk3 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(613,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk4 @ c @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[85,584]) ).
thf(636,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk1 )
| ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[613]) ).
thf(651,plain,
sk2 != zero,
inference(simp,[status(thm)],[636]) ).
thf(24,plain,
zero @ ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ),
inference(cnfConj,[status(thm)],[20]) ).
thf(289,plain,
zero @ ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ),
inference(rewrite,[status(thm)],[24,31]) ).
thf(15,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(80,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(81,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[81]) ).
thf(106,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,22]) ).
thf(110,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(114,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(240,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,114]) ).
thf(241,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(251,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ addition ) )
!= zero )
| ( A != sk3 )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(261,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[251]) ).
thf(21,plain,
sk4 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(612,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk4 @ c @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,584]) ).
thf(639,plain,
! [A: $i] :
( ( A != sk2 )
| ( A != sk1 )
| ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[612]) ).
thf(654,plain,
sk2 != sk1,
inference(simp,[status(thm)],[639]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(44,plain,
! [A: $i] :
( ( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(275,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,129]) ).
thf(276,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(282,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk3 )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(286,plain,
( ( sk1 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(120,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,23]) ).
thf(123,plain,
! [A: $i] :
( ( ( sk4 @ c )
!= zero )
| ( A
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(130,plain,
( ( ( sk4 @ c )
!= zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(104,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,22]) ).
thf(108,plain,
! [A: $i] :
( ( ( sk4 @ c )
!= zero )
| ( A
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(112,plain,
( ( ( sk4 @ c )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(137,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( ( sk4 @ c )
!= zero )
| ~ $true
| ( ( sk4 @ c )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[130,112]) ).
thf(138,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( ( sk4 @ c )
!= zero ) ),
inference(simp,[status(thm)],[137]) ).
thf(139,plain,
( ( sk4 @ c )
!= zero ),
inference(pattern_uni,[status(thm)],[138:[]]) ).
thf(290,plain,
zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ),
inference(rewrite,[status(thm)],[23,31]) ).
thf(51733,plain,
$false,
inference(e,[status(thm)],[56,52,89,85,65,53,77,86,531,640,43,671,19,79,83,288,37,25,651,289,261,29,21,28,38,654,129,41,32,34,584,44,286,80,35,50,31,40,26,114,139,290,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE035+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n017.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 19:11:17 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.83/1.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.33 % [INFO] Parsing done (272ms).
% 1.21/1.35 % [INFO] Running in sequential loop mode.
% 1.91/1.86 % [INFO] eprover registered as external prover.
% 1.91/1.87 % [INFO] Scanning for conjecture ...
% 2.08/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.24/2.12 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.41/2.15 % [INFO] Problem is first-order (TPTP FOF).
% 2.41/2.15 % [INFO] Type checking passed.
% 2.41/2.15 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 73.99/17.15 % External prover 'e' found a proof!
% 73.99/17.16 % [INFO] Killing All external provers ...
% 73.99/17.16 % Time passed: 16558ms (effective reasoning time: 15797ms)
% 73.99/17.16 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 73.99/17.16 % Axioms used in derivation (16): additive_identity, test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, right_annihilation, additive_idempotence, additive_associativity, order, additive_commutativity, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 73.99/17.16 % No. of inferences in proof: 114
% 73.99/17.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16558 ms resp. 15797 ms w/o parsing
% 60.38/17.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 60.38/17.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------